Riemann surface - question

Let f_0 denote the branch of ((z^2) - 1)^(1/2) defined on the sheet R_0, and show that the branches g_0 and g_1 of g on the two sheets are given by the equations:

g_0(z) = 1/g_1(z) = z + f_0(z)

OK. I see that it makes sense that g_0(z) = z + f_0(z). However, I don't quite see how it is also true that g_0(z) = 1/g_1(z). Any tips/explanations for why this is true will be greatly apprciated! I am quite stuck on this problem!

Ah, I see it now! Thank you so much! I converted the expression to polar coordinates (which I normally do for all roots of complex numbers), and this is what made it somewhat difficult for me to see this rather obvious answer.